The document provides information and examples about place value concepts including: - Place value means the value of a digit depends on its position in the number. - Numbers can be written in standard, expanded, and decimal forms. - Steps for comparing and ordering numbers include lining them up and comparing digits left to right. - Rounding involves underlining the place value to round to and adjusting the underlined digit up or down based on the digit to its right.

1. Understanding Place Value

2. Concepts & Practice Name That Place & Value Whole Numbers Standard Form Whole Numbers Expanded Form Whole Numbers Compare and Order Whole Numbers Vocabulary Word First Definition First Rounding Whole Numbers

3. Place & Value Place Value means that the amount a digit is worth depends on its position in the number. On a place-value chart, you can think of numbers in groups of three. Organizing the digits of a number in a place-value chart helps you understand the number’s value. Let’s Take a Look…

4. Ones Ones Tens Hundreds , Thousands Ones Tens Hundreds

5. By using the place value chart, we can determine the place and value of any digit within a number. Ones , Thousands O T H O T H 8 9 2 4 0 9 So, in the number 892,409, the place of the digit 2 is “Thousands” and the value is 2,000.

6. Let’s try using the chart! Ones , Thousands O T H O T H 7 4 3 1 8 6 What is the place of the digit 4? Ten-Thousands What is the value of the digit 4? 40,000 What is the place of the digit 5? Millions What is the value of the digit 5? 5,000,000 What is the value of the digit 6? 6 What is the place of the digit 7? Hundred-Thousands

7. Let’s practice without the chart! 234,745 6,098,139 807 2,391 8,620

8. THINK… What can I do to be sure I don’t make a careless mistake when trying to figure out a digit’s place and value?

9. Place & Value - Decimals Place Value means that the amount a digit is worth depends on its position in the number. This can be done with whole numbers and decimals. A decimal is a number expressed using a decimal point. Let’s Take a Look…

10. Let’s practice without the chart! .740 8,139.75 .328 23.81 .976

11. Standard Form Standard Form simply means the number is shown in the usual way we write a number. For example, “two thousand, eight hundred and sixty one” in standard form is 2,861! Simple enough! But beware of going to quickly and making a careless mistake!

12. Standard Form When we read numbers, it helps to think of them in the groups of three (periods) we use in our place value chart. The number “32,567,097” is read “thirty-two million, five hundred sixty seven thousand, and ninety seven”.

13. Try “reading” these numbers! 54,235,765 4,000,006 999,045 78,090 123,405,000 78,090 50,013,076 9,007,073

14. See if you can write these numbers in standard form ! Nineteen thousand, one hundred fifty Three million, sixty one thousand, three hundred two Twenty million, seventy six Three hundred seventy two thousand, eighty nine

15. THINK… What do you think is the most common mistakes students will make when converting a number from words to standard form?

16. Try “reading” these numbers! 35,463.7 4,000,006 238,004.09 8.879 1.876 67.9 64.011 1,234,535.5

17. See if you can write these numbers in standard form ! Two hundred seventy eight and one hundred thirty three thousandths Four hundred one and five thousandths Three thousand seven and six tenths Seventy five and fifty one hundredths

18. Expanded Form Expanded Form means writing a number as the sum of the value of its digits. Basically, you split the number up into the separate value of each digit and connect them with addition. Let’s Take a Look…It’s easier than it sounds!

19. 342 in expanded form is: 300 + 40 + 2 23,405 in expanded form is: 20,000 + 3,000 + 400 + 5 Ready to try some on your own? ***Notice in this example, there is a zero in the “tens” place, so we can just leave it out of our expanded notation!*** 607,094 in expanded form is: 600,000 + 7,000 + 90 + 4

20. Try “expanding” these numbers! 35,765 4,000,006 999,045 78,090 123,405,000 205,002 50,013,076 34,661

21. THINK… What are some “tricks” for breaking a number into expanded form without making any careless mistakes?

22. Expanded Form with Decimals Expanded Form means writing a number as the sum of the value of its digits. You handle expanded form with decimals the exact same way you do with whole number—break apart each digit’s value and connect them with addition! Let’s Try a Few…

23. 13.875 in expanded form is: 10 + 3 + .8 + .07 + .005 23.405 in expanded form is: 20 + 3 + .4 + .005 Ready to try some on your own? ***Notice in this example, there is a zero in the “hundredths” place, so we can just leave it out of our expanded notation!*** 607.094 in expanded form is: 600 + 7 + .09 + .004

24. Try “expanding” these numbers! 305.765 4.006 99.945 .093 123.405 25.002 513.076 34.661

25. Comparing Numbers Putting numbers in order from greatest to least or least to greatest is a skill you are guaranteed to use for the rest of your life. Just think: One day you might have to say “Wow! Last year I made $15,023,932 and this year I made $15,203,932!” It’s important to be able to rank and compare numbers. Let’s Explore…

27. Memorize the “RULE” for place value: Line Up, Or Mess Up! If we were comparing the numbers 32,624 and 32,094 first we would line them up! 32,624 32,094 Next, start from the left and compare each digit!

28. If we you are comparing 2 numbers that don’t have the same number of digits, you can always add a place holder zero if that makes it easier! 9,789 12,103 Remember: Line them up, then start from the left and compare each digit! 0

29. 6,927 6,899 31,203 300,102 200,300 200,030

30. Put these numbers in order from Least to Greatest ! Before we even begin to tackle this, what do you think is the MOST common mistake students make on this type of problem? 543 1,333 534 17,430 17,330 17,309 53,302 8,032 102,000

31. Put these numbers in order from Greatest to Least ! 245,505 245,055 244,955 1,230 999 2,310 9,080 9,800 9,900

33. Remember, if the numbers you are comparing don’t don’t have the same number of digits, you can always add a zero as a place holder! 2.003 12.103 Remember: Line them up, then start from the left and compare each digit! 0

34. .809 .810 41.203 400.102 6.320 6.317

35. Put these numbers in order from Least to Greatest ! Remember: The most common mistake students make is reversing the order of least to greatest and vice versa! Don’t fall in that trap! Check and re-check yourself! 2.32 3.31 .484 13.43 13.33 14.03 6.09 5.99 6.91

36. Put these numbers in order from Greatest to Least ! 745.505 545.955 744.355 1.230 .999 2.310 9.080 9.800 9.900

37. Decimal A decimal number is a number that has a whole number part and a fractional whole number part. In general, the numbers to the left of the decimal point make up the whole part of the number, and the numbers to the right of the decimal point make up the fractional whole part of the number For example, the decimal number 658.125 has a whole part of 658 and a fractional whole part of 125.

38. Decimal Point A dot written in a number that separates the whole number from the fractional part; it is read as “and”

39. Expanded Form Numbers broken up into their individual place values. (ie: 234 = 200 + 30 + 4)

40. Greater The number that is bigger in quantity or amount

41. Integer A member of the set of whole numbers and their opposites; Positive and negative whole numbers and zero; NOT fractions, decimals or mixed numbers … -3, -2, -1, 0, 1, 2, 3…

42. Less The number that is smaller in amount or quantity

43. Place Value The value given to the space a digit holds because of its place in the numeral

44. Rounding Replacing a number with an estimate of that number to a given place value

45. Standard Form A number written using digits

46. Whole Number A positive number without a fraction or decimal part

47. Decimal A decimal number is a number that has a whole number part and a fractional whole number part. In general, the numbers to the left of the decimal point make up the whole part of the number, and the numbers to the right of the decimal point make up the fractional whole part of the number For example, the decimal number 658.125 has a whole part of 658 and a fractional whole part of 125.

48. Decimal Point A dot written in a number that separates the whole number from the fractional part; it is read as “and”

49. Expanded Form Numbers broken up into their individual place values. (ie: 234 = 200 + 30 + 4)

50. Greater The number that is bigger in quantity or amount

51. Integer A member of the set of whole numbers and their opposites; Positive and negative whole numbers and zero; NOT fractions, decimals or mixed numbers … -3, -2, -1, 0, 1, 2, 3…

52. Less The number that is smaller in amount or quantity

53. Place Value The value given to the space a digit holds because of its place in the numeral

54. Rounding Replacing a number with an estimate of that number to a given place value

55. Standard Form A number written using digits

56. Whole Number A positive number without a fraction or decimal part

57. Rounding When you “round” numbers, you are replacing the number with an estimate to a given place value. Rounding can help you simplify a problem in order to do mental math or get an estimate of your final answer. There are 3 simple steps…

58. Step 1 Underline the place to which you want to round. 24,761 A word of caution: These steps might seem too “easy”, once you get used to rounding, but do them anyways! It will ensure that you don’t make a careless mistake!

59. Step 2 Circle the digit to the right of the underlined digit. 24,761 Think of the circled number as a telescope directing you where to go next in the problem!

60. Step 3 If your circled digit is 0 – 4 the underlined number will stay the same . If the circled digit is 5 – 9 then the underlined number will go up one ! 24,761 All of the numbers to the right of the underlined number will turn to zeros! 24,800

61. 935 940 Let’s Practice a Few! Round to the Tens Place 1,348 1,300 Round to the Hundreds Place

62. 6,608 6,610 Let’s Practice a Few! Round to the Tens Place 472 500 Round to the Hundreds Place

63. 782 Now, Your Turn! Round to the Tens Place 14,762 Round to the Thousands Place 93 Round to the Hundreds Place 185,112 Round to the Ten Thousands Place

64. Rounding with Decimals Rounding with decimals is done exactly the same way you do it with whole numbers. Notice as we practice these next problems how important it is to know your places!

65. Step 1 Underline the place to which you want to round. 57.146

66. Step 2 Circle the digit to the right of the underlined digit. 57.146 Think of the circled number as a telescope directing you where to go next in the problem!

67. Step 3 If your circled digit is 0 – 4 the underlined number will stay the same . If the circled digit is 5 – 9 then the underlined number will go up one ! 57.146 All of the numbers to the right of the underlined number will turn to zeros! 57.150

68. 8.452 8.500 Let’s Practice a Few! Round to the Tenths Place .728 .730 Round to the Hundredths Place

69. 3.49 3.00 Let’s Practice a Few! Round to the Ones Place 9.351 9.400 Round to the Tenths Place

70. .068 Now, Your Turn! Round to the Tenths Place 14.762 Round to the Ones Place 5.517 Round to the Hundredths Place 392.503 Round to the Tenths Place

71. Which number has 4 in the hundred thousands place? 4,034,004 3,408,073 4,046,488

72. Which number has 6 in the thousandths place? 5.603 6.600 6.536

73. Which of the following shows thirty-two million, five hundred thirty-two thousand? 32,000,532 32,005,320 32,532,000

74. Which of the following shows eighty-nine and seventy-two hundredths? 89.72 897.2 89.072

75. Which number has 8 in the thousands place? 253,080,923 280,825,808 28,438,088

76. Which shows the numbers in order from least to greatest? 131,303 113,003 313,011 103,010 100,333 330,001 31,010 111,303 301,033

77. Which number is read seventy-one and eighteen hundredths? 71.018 71.18 7.118

78. Which of the following is true? 89,909 > 89,099 200,200 > 202,000 52,010 < 4,999

79. Which of the following is true? 0.105 > 0.15 0.05 < 0.015 .005 < .100

80. How is the number 412,030 read? four hundred twelve thousand, three four hundred thousand, twelve, thirty four hundred twelve thousand, thirty

81. What is 35.042 rounded to the nearest ten? 40.000 35.000 30.000

82. What is 5.892 rounded to the nearest tenth? 5.890 5.900 6.000

83. What is 253.765 rounded to the nearest hundredth? 300.000 253.770 253.800